miser

The Miser Project
Computation Theory

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0.1.1 2025-09-12T16:36Z

Synopsis

This topic is devoted to application of Computation Theory, including confirmation of the Church-Turing completeness of oMiser. Elements of Automata Theory and Complexity Theory are touched on, along with application of Computability Theory with respect to oMiser and thence to Miser generally.

With regard to Church-Turing completeness, are three important computation-theoretical claims to be made and demonstrated about the ‹ob› Universal Computational function obap.ap(p, x) and the companion function obap.eval(p).

  1. Claim: obap..ap is a universal function in the sense that for every computable function f(x) on obs x there is an ob p for which obap.ap(p, x) = f(x) for every determined ob x.
  2. Claim: The obs are denumerably infinite (i.e., are countable) and ‹ob› can represent the natural numbers, N, and their arithmetic. This puts ‹ob› with obap.ap on par with other schemes, including Universal Turing Machines, that satisfy Church’s Thesis on effective computability.
  3. Claim: A feature of universal computation systems is any one can simulate the others. This is demonstrationed for ‹ob› by representation of a Universal Turing Machine, a roundabout confirmation of Claim 1.

This topic carries details of the historical and technical conditions by which these claims are demonstrated, and precisely what they signify.

Catalog (Specimens, draft notes, ctYYMMXX Content TBD)

This placeholder links to raw materials and notes, including text files. There will be organized folios of content as documentation continues.

ID Status Started Topic
Diary & Job Jar undated 2025-09-12 Notes until there is more narrative material

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